Predatorprey dynamics with hunger structure
22/09/2021 Wednesday 22nd September 2021, 16:00 ()
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Paulo Amorim, Instituto de Matemática  Universidade Federal do Rio de Janeiro
We present, analyse and simulate a model for predatorprey interaction with hunger structure. The model consists of a nonlocal transport equation for the predator, coupled to an ODE for the prey. We deduce a system of 3 ODEs for some integral quantities of the transport equation, which generalises some classical LotkaVolterra systems. By taking an asymptotic regime of fast hunger variation, we find that this system provides new interpretations and derivations of several variations of the classical LotkaVolterra system, including the Hollingtype functional responses. We next establish a wellposedness result for the nonlocal transport equation by means of a fixedpoint method. Finally, we show that in the basin of attraction of the nontrivial equilibrium, the asymptotic behaviour of the original coupled PDEODE system is completely described by solutions of the ODE system [SIAM J. Appl. Math., 80(6), 26312656 (2020)].
